Analytical Chem istry - DePauw University

454 Analytical Chemistry 2.0A second approach for determining a weak acid’s pK a is to use a Granplot. For example, earlier in this chapter we derived the following equationfor the titration of a weak acid with a strong base.[ HO+ ] × V = K V − K V3 b a eq a bA plot of [H 3 O + ] V b versus V b , for volumes less than the equivalencepoint, yields a straight line with a slope of –K a . Other linearizations havebeen developed which use the entire titration curve, or that require no assumptions.6 This approach to determining acidity constants has been usedto study the acid–base properties of humic acids, which are naturally occurring,large molecular weight organic acids with multiple acidic sites. In onestudy a humic acid was found to have six titratable sites, three of which wereidentified as carboxylic acids, two of which were believed to be secondary ortertiary amines, and one of which was identified as a phenolic group. 79B.7 Evaluation of Acid–Base TitrimetrySc a l e o f Op e r a t i o nAcid–base titrimetry is an example of a totalanalysis technique in which the signalis proportional to the absolute amount ofanalyte. See Chapter 3 for a discussion ofthe difference between total analysis techniquesand concentration techniques.In an acid–base titration the volume of titrant needed to reach the equivalencepoint is proportional to the moles of titrand. Because the pH of thetitrand or the titrant is a function of its concentration, however, the changein pH at the equivalence point—and thus the feasibility of an acid–basetitration—depends on their respective concentrations. Figure 9.23, for example,shows a series of titration curves for the titration of several concentrationsof HCl with equimolar solutions NaOH. For titrand and titrantconcentrations smaller than 10 –3 M, the change in pH at the end pointmay be too small to provide accurate and precise results.6 (a) Gonzalez, A. G.; Asuero, A. G. Anal. Chim. Acta 1992, 256, 29–33; (b) Papanastasiou, G.;Ziogas, I.; Kokkindis, G. Anal. Chim. Acta 1993, 277, 119–135.7 Alexio, L. M.; Godinho, O. E. S.; da Costa, W. F. Anal. Chim. Acta 1992, 257, 35–39.pH14121086(a)(b)(c)(d)(e)4Figure 9.23 Titration curves for 25.0 mL of (a) 10 –1 MHCl, (b) 10 –2 M HCl, (c) 10 –3 M HCl, (d) 10 –4 MHCl, and (e) 10 –5 M HCl. In each case the titrant is anequimolar solution of NaOH.200 10 20 30 40 50Volume of NaOH (mL)